Question

The hypotenuse of a right triangle is 45 inches,which one of the sides being 18 inches. Find the midding side length. Round to the nearest hindredth if necessary.

Answer 1

Hello!

The answer is:

The missing side length is 41.24 inches.

Why?

Since we are working with a righ triangle, to solve this problem we can use the Pythagorean Theorem.

The Pythagorean Theorem states that:

`Hypotenuse^(2)=(Side_(1))^(2)+(Side_(2))^(2)`

We are given that:

`Hypotenuse=45in\\Side_(1)=18in`

So, isolating the missing side and substituting the given information, we have:

`(45in)^(2)=(18in)^(2)+(Side_(2))^(2)`

`(Side_(2))^(2)=(45in)^(2)-(18in)^(2)+`

`\sqrt{(Side_(2))^(2)} =\sqrt{(45in)^(2)-(18in)^(2)}\\\\Side_(2)=\sqrt{2025in^(2)-324^(2)}=\sqrt{1701^(2)}\\\\Side_(2)=41.2431in=41.24in`

Have a nice day!

Answer 2

The length of the missing side is 41.24 inches

Explanation:

* Lets talk about the Pythagoras theorem

- It used in the right angle triangle

- The hypotenuse is the opposite side to the right angle and it's the

longest side in the triangle

- The two other sides in the right angle triangle are the legs of

the right angle

- If the length of the hypotenuse is c units and the lengths of the

two legs of the right angle area a and b

∴ a² + b² = c² ⇒ c = √(a² + b²)

* Now lets solve the problem

∵ The length of the hypotenuse = 45 inches

∵ The length of one legs of the right angle = 18 inches

- Lets use the Pythagoras theorem

∴ c² = a² + b²

∴ 45² = 18² + b² ⇒ subtract 18² from both sides

∴ b² = 45² - 18² = 2025 - 324 = 1701 ⇒ take square root for both sides

∴ b = √1701 = 41.24 inches